Gamma = dfracpartial^2 Vpartial S^2 = dfracpartial Δpartial S — convexity in S, and the rate at which a delta-hedge degrades. Maximal for ATM options near expiry, Gamma_call = dfracφ(d_1)Sσ√(T). Long gamma earns from realised variance (tfrac12Gamma,(Δ S)^2 per discrete step) but pays theta in calm markets; short gamma is the inverse — large dealers running short-gamma books force mechanical buying as the underlying rises (gamma-driven feedback, notable in S&P 500 dealer-positioning literature).